A regional telephone company operates three identical relay stations at different locations. During a one-year period, the number of malfunctions reported by each station and the causes are shown below. $$ \begin{array}{lccc} {\text { Station }} & \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} \\ \hline \text { Problems with electricity supplied } & 2 & 1 & 1 \\ \text { Computer malfunction } & 4 & 3 & 2 \\ \text { Malfunctioning electrical equipment } & 5 & 4 & 2 \\ \text { Caused by other human errors } & 7 & 7 & 5 \end{array} $$ Suppose that a malfunction was reported and it was found to be caused by other human errors. What is the probability that it came from station $C ?$
Added by Rachel G.
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This is 7 (from station A) + 7 (from station B) + 5 (from station C) = 19. Show more…
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Regional telephone company operates three identical relay stations at different locations. During a one-year period, the probability of malfunctions reported by each station and the causes are shown below A B C problem with electricity supply 5% 3% 1% Computer malfunction 9% 7% 5% malfunctioning equipment 12% 9% 5% caused by human errors 16% 16% 12% Suppose that a malfunction was reported and it was found to be caused by other human errors. What is the probability that it came from station C?
David N.
The relay network below operates if and only if there is a closed path of relays from point a to b. Assume that relays fail independently and that the probabilities of failure for the three relays are, respectively, P(C1 fails)=0.1, P(C1 works)=0.9, P(C2 fails)=0.2, P(C2 works)=0.8, P(C3 fails)=0.25, P(C3 works)=0.75. What is the probability that the relay network operates? Explain your assumptions.
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A transmitter is sending a message by using a binary code, namely, a sequence of 0 and 1 s. Each transmitted bit $(0$ or 1$)$ must pass through three relays to reach the receiver. At each relay, the probability is. 20 that the bit sent will be different from the bit received (a reversal). Assume that the relays operate independently of one another. Transmitter $\rightarrow$ Relay 1$\rightarrow$ Relay 2$\rightarrow$ Relay 3$\rightarrow$ Receiver (a) If a 1 is sent from the transmitter, what is the probability that a 1 is sent by all three relays? (b) If a 1 is sent from the transmitter, what is the probability that a 1 is received by the receiver? [Hint: The eight experimental outcomes can be displayed on a tree diagram with three generations of branches, one generation for each relay. (c) Suppose 70$\%$ of all bits sent from the transmitter are 1 s. If a 1 is received by the receiver, what is the probability that a 1 was sent?
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